Efficient Infrastructure Restoration Strategies Using the Recovery Operator

Abstract

Infrastructure systems are critical for society's resilience, government operation, and overall defense. Thereby, it is imperative to develop informative and computationally efficient analysis methods for infrastructure systems, which reveal system vulnerabilities and recoverability. To capture practical constraints in systems analyses, various layers of complexity play a role, including limited element capacities, restoration resources, and the presence of interdependence among systems. High‐fidelity modeling such as mixed integer programming and physics‐based modeling can often be computationally expensive, making time‐sensitive analyses challenging. Furthermore, the complexity of recovery solutions can reduce analysis transparency. An alternative, presented in this work, is a reduced‐order representation, dubbed a recovery operator, of a high‐fidelity time‐dependent recovery model of a system of interdependent networks. The form of the operator is assumed to be a time‐invariant linear dynamic model apt for infrastructure restoration. The recovery operator is generated by applying system identification techniques to numerous disaster and recovery scenarios. The proposed compact representation provides simple yet powerful information regarding systemic recovery dynamics, and enables generating fast suboptimal recovery policies in time‐critical applications.

Integrating Operational and Organizational Aspects in Interdependent Infrastructure Network Recovery

“…However, they did not consider the existence of diverse limited resources or the possible savings associated with recovering multiple colocated components. González et al (2017) proposed a general mathematical formulation, denominated the td-INDP. The td-INDP allows determining the minimum-cost recovery strategy for a system of interdependent networks while considering multiple operational constraints such as diverse limited resources, the existence of shared spaces between multiple colocated components, and the existence of multiple types of interdependencies.…”

“…This section presents a general structure of recovery models proposed in the literature to contextualize typical objective functions and constraints. Without loss of generality, the notation is consistent with the INDP proposed by González et al (2016) and its time-dependent extension (i.e., the td-INDP in González et al, 2017), which is an optimization approach to restore damaged infrastructure networks in which the functionality of nodes may depend on that of nodes in other networks.…”

“…The main variables in the model are w it and y i jt , which are binary decisions on whether to repair node i, or arc (i, j), at time t, respectively; variables w it and y i jt state whether a node or arc is functional at time t, depending on damage states and repair decisions (i.e., a damaged component does not become functional unless it is repaired). Variables x i jlt represent the flow of commodity l through arc (i, j) at time t, whereas δ + ilt and δ − ilt , which appear as auxiliary variables in González et al (2017), are crucial in our analysis, since they represent over-and undersupply (respectively) of commodity l at node i and time t. The primary role of δ + ilt is to keep track of excess commodity at production nodes whenever flow cannot be delivered due to damage at arcs and/or consumption nodes. For instance, if all arcs were damaged (prohibiting all flows), then δ + ilt would absorb excess at production nodes, whereas δ − ilt would absorb shortage at consumption nodes, in order to honor the equality in flow balance constraints.…”

“…However, note that the proposed methods and analysis could also be used in conjunction with other recovery-oriented mixed integer programming (MIP) models (Cavdaroglu, Hammel, Mitchell, Sharkey, & Wallace, 2011;Lee II, Mitchell, & Wallace, 2007;Nurre, Cavdaroglu, Mitchell, Sharkey, & Wallace, 2012). Our proposal extends the ideas from González et al (2017) in two main ways. First, our contribution focuses on how operational models can contribute to broader policy analysis of resilience, rather than focusing on specific aspects of an optimization problem.…”

“…To demonstrate our framework, we adopt the Interdependent Network Design Problem (INDP) (González, Dueñas-Osorio, Sánchez-Silva, & Medaglia, 2016), because of its comprehensive set of constraints, and the time-dependent feature incorporated in González, Chapman, Dueñas-Osorio, Mesbahi, and D'Souza (2017), which is useful for our proposals in Section 4.1. However, note that the proposed methods and analysis could also be used in conjunction with other recovery-oriented mixed integer programming (MIP) models (Cavdaroglu, Hammel, Mitchell, Sharkey, & Wallace, 2011;Lee II, Mitchell, & Wallace, 2007;Nurre, Cavdaroglu, Mitchell, Sharkey, & Wallace, 2012).…”